Answer on Mechanics | Relativity Question for brett

2011-10-25T08:42:38-0400

Question #4823

A daredevil jumps a canyon 12 m wide. To do so, he drives a car up a 10 incline. What minimum speed must he achieve to clear the canyon? The acceleration of gravity is 9.81 m/s2 . Answer in units of m/s

Expert's answer

2012-05-22T12:12:16-0400

To find this, you must first find the peak altitude which occurs atthe moment his vertical velocity is zero.Vy(t) = Vyo -gt = 0 =&gt; t = Vyo/gWe know the time from ground to peak altitude is equal to the timefrom peak altitude to ground. So the total time of flight is 2*t =2*Vyo/g.The distance the car travels is Vxo*2*t = Vxo*2*Vyo/g = 12 meters.Use tan10=Vyo/Vxo =&gt; Vyo = Vxo*tan10Substitute into the distance equation:[2*Vxo^2*tan10]/g = 12Vxo = sqrt[12g/2*tan10] = sqrt[117.72 / 0.3527] = 18.27 m/s, but thatis just the horizontal componentVo = Vxo/cos10 = 18.55 m/s